Surf-riding of a Ship in Regular Seas

Abstract

This paper discusses critical conditions of surf-riding of a ship in regular following seas. The authors carried out time domains simulations of ship longitudinal motion in regular following seas and presented those results as phase trajectories. The ordinate of the phase plane is instantaneous velocity of the ship and the abscissa is relative position of the ship to wave. The phase trajectories showed three different patterns of the motion. The trajectories with a periodic attractor represent "perlodic surging motion". Those with point attractors represent "surf-riding under any initial conditions". And those with both point attractors and a perlodic attractor represent "surf-riding under certain initial conditions". Further those trajectories indicate that a ship self-propelled with constant revolution in regular seas does not suffer the surf-riding under certain initial conditions". The critical velocity of the "surf-riding under any initial conditions" predicted by separatrices on the phase plane agreed with that measured by free running model experiments. In the ligtht of the separatrices, we can easily recognize that the critical condition proposed by Grim is identical to that by Kan and valid for "surf-riding under any initial conditions." In addition, we pointed out that surf-riding remarkably reduces rudder force as propeller advance coefficient increases.